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%I #5 Jun 04 2014 13:43:51
%S 4,6,5,6,3,8,6,4,6,7,7,9,0,7,5,7,3,7,1,0,9,9,7,5,9,1,0,2,6,4,2,9,0,5,
%T 7,4,6,3,2,5,5,0,1,4,6,1,7,4,3,4,8,3,8,9,3,5,6,0,0,9,9,0,1,9,1,7,6,5,
%U 1,3,9,2,6,1,0,8,8,0,4,7,7,5,6,9,3,4,0,6,6,6,1,8,9,8,4,9,7,3,8,8,6,1,5,9
%N Decimal expansion of 'etaHat', a constant used in the asymptotic evaluation of e.g.f. coefficients for the number of labeled mobiles.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.6 Otter's tree enumeration constants, p. 303.
%F A038037 = Numerator of n-th coefficient ~ etaHat * xiHat^n * n^(n-1), where xiHat is A243395.
%e 0.46563864677907573710997591026429...
%t digits = 104; mu = x /. FindRoot[x/(1 - x) == 1 + Log[1/(1 - x)], {x, 1/2}, WorkingPrecision -> digits + 5] ; etaHat = Sqrt[mu*(1 - mu)]; RealDigits[etaHat, 10, digits] // First
%Y Cf. A038037, A242769, A243395.
%K nonn,cons
%O 0,1
%A _Jean-François Alcover_, Jun 04 2014
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